UXarray for Advanced HEALPix Analysis & Visualization

In this section, you’ll learn:

Using the uxarray package to perform advanced analysis operators over HEALPix data such as non-conservative zonal means, etc.

Prerequisites

Concepts	Importance	Notes
UXarray	Necessary
HEALPix overview	Necessary

Time to learn: 30 minutes

import cartopy.crs as ccrs
import holoviews as hv
import intake
import uxarray as ux

Rasterized Point Plots

When working with a higher-resolution dataset at a global scale, it’s not always practical to render each cell as a polygon. Instead, we can rasterize the center of each pixel.

# Controls the size of each pixel (smaller value leads to larger pixels)
pixel_ratio = 0.5

uxda.isel(time=0).plot.points(
    projection=ccrs.Robinson(),
    rasterize=True,
    dynamic=False,
    width=700,
    pixel_ratio=pixel_ratio,
    cmap="inferno",
    title=f"Global Air Temperature, pixel_ratio={pixel_ratio}",
)

WARNING:param.GeoRasterPlot00785: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

If we decrease the size of each pixel (by setting the pixel ratio to a higher value), we can start to see missing values, which is due to a lower density of points near the poles, leading to some pixels not containing any of our original points.

Because of this, it’s useful to try a few pixel_ratio values and see which one works best for your given resolution.

# Controls the size of each pixel (smaller value leads to larger pixels)
pixel_ratio = 2.0

uxda.isel(time=0).plot.points(
    projection=ccrs.Robinson(),
    rasterize=True,
    dynamic=False,
    width=700,
    pixel_ratio=pixel_ratio,
    cmap="inferno",
    title=f"Global Air Temperature with bad pixel size selection, pixel_ratio={pixel_ratio}",
)

WARNING:param.GeoRasterPlot00982: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

Cross-Sections

UXarray provides several spatial cross-section methods:

Constant-Latitude Slice Extract data along a fixed latitude.
Constant-Longitude Slice Extract data along a fixed longitude.
Latitudinal-Interval Slice Extract data between two latitude bounds.
Longitudinal-Interval Slice Extract data between two longitude bounds.

To illustrate, we’ll use a zoom level of `4.

uxda_coarse = ux.UxDataset.from_healpix(model_run(zoom=4, time="P1D").to_dask())["tas"]

/home/runner/miniconda3/envs/healpix-cookbook-dev/lib/python3.10/site-packages/intake_xarray/base.py:21: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
  'dims': dict(self._ds.dims),

Constant Latitude

boulder_lat = 40.0190

uxda_cross_lat = uxda_coarse.cross_section.constant_latitude(boulder_lat)

uxda_cross_lat.isel(time=0).plot(
    rasterize=False,
    projection=ccrs.Robinson(),
    global_extent=True,
    cmap="inferno",
    features=["coastline"],
    title=f"Global temperature cross-section at {boulder_lat} degrees latitude",
    width=700,
    colorbar=False,
)

WARNING:param.GeoOverlayPlot01102: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

Since cross sections return a new instance of our data, we can perform operations directly on them.

print(
    f"Mean at {boulder_lat} degrees lat (Boulder, CO, USA): {uxda_cross_lat.mean().values} K"
)

Mean at 40.019 degrees lat (Boulder, CO, USA): 286.6632080078125 K

Latitude Interval

uxda_lat_interval = uxda_coarse.cross_section.constant_latitude_interval(
    [boulder_lat - 15, boulder_lat + 15]
)

uxda_lat_interval.isel(time=0).plot(
    rasterize=False,
    projection=ccrs.Robinson(),
    global_extent=True,
    cmap="inferno",
    clim=(220, 310),
    features=["coastline"],
    title=f"Global temperature cross-section at the latitude interval [{boulder_lat-5},{boulder_lat+5}] degrees",
    width=700,
    colorbar=False,
)

WARNING:param.GeoOverlayPlot01276: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

print(
    f"Mean at the latitude interval of [{boulder_lat-5},{boulder_lat+5}] degrees (-/+15 degrees Boulder, CO, USA): {uxda_lat_interval.mean().values} K"
)

Mean at the latitude interval of [35.019,45.019] degrees (-/+15 degrees Boulder, CO, USA): 286.2819519042969 K

Non-Conservative Zonal Mean

Calculating the zonal mean is easy by providing the latitude range between -90 and 90 degrees with a step size in degrees:

zonal_mean_tas = uxda.isel(time=0).zonal_mean(lat=(-90, 90, 5))

(
    uxda.isel(time=0).plot(
        cmap="inferno",
        # periodic_elements="split",
        height=300,
        width=600,
        colorbar=False,
        ylim=(-90, 90),
    )
    + zonal_mean_tas.plot.line(
        x="tas_zonal_mean",
        y="latitudes",
        height=300,
        width=180,
        ylabel="",
        ylim=(-90, 90),
        xlim=(220, 310),
        # xticks=[220, 250, 280, 310],
        yticks=[-90, -45, 0, 45, 90],
        grid=True,
    )
).opts(title="Temperature and its Zonal means at every 5 degrees latitude")

Remapping & Custom Grid Topology

Now, let’s take a look at an example of UXarray’s remapping functionality. UXarray currently supports two remapping methods:

Nearest Neighbor Assigns each target point the value of its closest source point.
Inverse Distance Weighted Computes each target point’s value as the weighted average of nearby source points, with weights inversely proportional to distance.

For this example, we’ll use the Nearest Neighbor approach.

Region of Interest: Chicago

Before remapping, we restrict our data to a 2.5°×2.5° bounding box centered on Chicago, Illinois.

chicago_lon = -87.6298
chicago_lat = 41.8781

degree_span = 2.5
half_span = degree_span / 2.0

Since we will be using this subset of data for remapping, let’s make the bounding box slightly larger than the extent of our destination grid.

degree_eps = 0.25
half_span_eps = half_span + degree_eps

healpix_subset = uxda.isel(time=0).subset.bounding_box(
    (chicago_lon - half_span_eps, chicago_lon + half_span_eps),
    (chicago_lat - half_span_eps, chicago_lat + half_span_eps),
)
healpix_subset.plot(
    title="Temperature Subset around Chicago (HEALPix zoom 9)",
    backend="matplotlib",
    width=500,
    height=500,
    aspect=2,
    cmap="inferno",
    features=["states", "rivers"],
)

/home/runner/miniconda3/envs/healpix-cookbook-dev/lib/python3.10/site-packages/cartopy/io/__init__.py:241: DownloadWarning: Downloading: https://naturalearth.s3.amazonaws.com/110m_cultural/ne_110m_admin_1_states_provinces_lakes.zip
  warnings.warn(f'Downloading: {url}', DownloadWarning)

/home/runner/miniconda3/envs/healpix-cookbook-dev/lib/python3.10/site-packages/cartopy/io/__init__.py:241: DownloadWarning: Downloading: https://naturalearth.s3.amazonaws.com/110m_physical/ne_110m_rivers_lake_centerlines.zip
  warnings.warn(f'Downloading: {url}', DownloadWarning)

Creating our Destination Grid

UXarray wraps SciPy’s mesh generation methods to support representing point cloud data build around the following algorithms

Delaunay Triangulation
Voronoi Tesselation

Let’s create a grid of points centered around Chicago and triangulate it to create our destination grid.

import numpy as np

n_points = 10

# Longitude Vector
lon_vals = np.linspace(
    chicago_lon - half_span, chicago_lon + half_span, n_points, dtype=np.float64
)

# Latitude Vector
lat_vals = np.linspace(
    chicago_lat - half_span, chicago_lat + half_span, n_points, dtype=np.float64
)

# Meshgrid
lon, lat = np.meshgrid(lon_vals, lat_vals)

# flatten for processing
lon_flat = lon.ravel()
lat_flat = lat.ravel()

# Create a mask of boundary points
min_lon, max_lon = lon_vals[0], lon_vals[-1]
min_lat, max_lat = lat_vals[0], lat_vals[-1]

mask = (
    np.isclose(lon_flat, min_lon)
    | np.isclose(lon_flat, max_lon)
    | np.isclose(lat_flat, min_lat)
    | np.isclose(lat_flat, max_lat)
)

boundary_points = np.flatnonzero(mask)

destination_grid = ux.Grid.from_points(
    (lon_flat, lat_flat),
    method="regional_delaunay",
    boundary_points=boundary_points,
)

destination_grid.plot(
    title="Triangulated Points (Destination Grid)",
    backend="matplotlib",
    width=500,
    height=500,
    aspect=2,
    features=["states", "rivers"],
)

Remapping

Now that we have both our subset of the original data and our custom destination grid, let’s remap!

uxda_remapped = uxda.isel(time=0).remap.nearest_neighbor(
    destination_grid, coord_type="cartesian"
)

/home/runner/miniconda3/envs/healpix-cookbook-dev/lib/python3.10/site-packages/uxarray/grid/coordinates.py:254: UserWarning: This cannot be guaranteed to work correctly on concave polygons
  warnings.warn("This cannot be guaranteed to work correctly on concave polygons")

/home/runner/miniconda3/envs/healpix-cookbook-dev/lib/python3.10/site-packages/uxarray/grid/coordinates.py:254: UserWarning: This cannot be guaranteed to work correctly on concave polygons
  warnings.warn("This cannot be guaranteed to work correctly on concave polygons")

(
    healpix_subset.plot(
        title="Temperature Subset around Chicago (HEALPix zoom 9)",
        backend="matplotlib",
        width=600,
        height=600,
        aspect=2,
        cmap="inferno",
        features=["states", "rivers"],
    )
    + uxda_remapped.plot(
        title="Remapped Temperature",
        backend="matplotlib",
        width=600,
        height=600,
        aspect=2,
        cmap="inferno",
        features=["states", "rivers"],
    )
).cols(1).opts(fig_size=150)

UXarray for Advanced HEALPix Analysis & Visualization

In this section, you’ll learn:

Prerequisites

Open data catalog

Create UXarray Datasets from HEALPix

Data variable of interest

Global mean and plot

Rasterized Point Plots

Cross-Sections

Constant Latitude

Latitude Interval

Non-Conservative Zonal Mean

Remapping & Custom Grid Topology

Region of Interest: Chicago

Creating our Destination Grid

Remapping

UXarray for Advanced HEALPix Analysis & Visualization

In this section, you’ll learn:

Related Documentation

Prerequisites

Open data catalog

Create UXarray Datasets from HEALPix

Data variable of interest

Global mean and plot

Rasterized Point Plots

Cross-Sections

Constant Latitude

Latitude Interval

Non-Conservative Zonal Mean

Remapping & Custom Grid Topology

Region of Interest: Chicago

Creating our Destination Grid

Remapping